A Robust Rotated-Hybrid Riemann Scheme for Multidimensional Inviscid Compressible Flows
Original Paper
First Online:
- 11 Downloads
Abstract
A robust algorithm is investigated for multidimensional inviscid compressible flows, based on rotated Riemann solver framework. Indeed, the proposed method combines the TV-HLL and Roe schemes. The upwind direction is imposed by the velocity-difference vector. Then, the TV-HLL solver is applied in the direction perpendicular to shocks in order to suppress carbuncle. In addition, the Roe solver is applied across shear layers to minimize the amount of dissipation. To assess the capabilities of the present method, numerous test problems (2D and 3D) are simulated.
Keywords
TV-HLL Roe Rotated Riemann scheme Inviscid flowsNotes
References
- 1.Godunov, S.K.: A difference scheme for numerical computation of discontinuous solutions of equations of fluid dynamics. Math. Sbornik 47, 271 (1959)zbMATHGoogle Scholar
- 2.Harten, A., Lax, P.D., Van Leer, B.: On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25, 35 (1983)MathSciNetCrossRefGoogle Scholar
- 3.Einfeldt, B.: On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 25, 294 (1988)MathSciNetCrossRefGoogle Scholar
- 4.Roe, P.L.: Approximate Riemann solvers, parameters vectors, and difference schemes. J. Comput. Phys. 43, 357–372 (1981)MathSciNetCrossRefGoogle Scholar
- 5.Quirk, J.J.: ICASE Report, pp. 92–64 (1992)Google Scholar
- 6.Steger, J.L., Warming, R.F.: Flux vector splitting of the inviscid gas dynamics equations with applications to finite difference methods. J. Comput. Phys. 40, 263–293 (1981)MathSciNetCrossRefGoogle Scholar
- 7.Anderson, W., Thomas, J.L., Van Leer, B.: Comparison of finite volume flux vector splittings for the Euler equations. AIAA J. 24, 1453–1460 (1986)CrossRefGoogle Scholar
- 8.Liou, M.S., Steffen, C.J.: A new flux splitting scheme. J. Comput. Phys. 107(1), 23–39 (1993)MathSciNetCrossRefGoogle Scholar
- 9.Liou, M.S., Wada, Y.: A flux splitting scheme with high-resolution and robustness for discontinuities. In: AIAA paper, No. 94–0083 (1994)Google Scholar
- 10.Liou, M.S.: A sequel to AUSM: AUSM+. J. Comput. Phys. 129, 364–382 (1996)MathSciNetCrossRefGoogle Scholar
- 11.Kim, K.H., Lee, J.H., Rho, O.H.: An improve of AUSM schemes by introducing the pressure-based weight functions. Comput. Fluids 27(3), 311–346 (1998)MathSciNetCrossRefGoogle Scholar
- 12.Kim, K.H., Kim, C., Rho, O.: Methods for accurate computations of hypersonic flows I. AUSMPW+ scheme. J. Comput. Phys. 174, 38–80 (2001)MathSciNetCrossRefGoogle Scholar
- 13.Liou, M.S.: A sequel to AUSM, Part II: AUSM+-up for all speeds. J. Comput. Phys. 214, 137–170 (2006)MathSciNetCrossRefGoogle Scholar
- 14.Edwards, J.R.: A low-diffusion flux-splitting scheme for Navier–Stokes calculations. Comput. Fluid 26, 635–659 (1997)MathSciNetCrossRefGoogle Scholar
- 15.Edwards, J.R., Franklin, R.K., Liou, M.S.: Low-diffusion flux-splitting methods for real fluid flows with phase transition. AIAA J. 38, 1624–1633 (2000)CrossRefGoogle Scholar
- 16.Ihm, S.W., Kim, C.: Computations of homogeneous-equilibrium two-phase flows with accurate and efficient shock-stable schemes. AIAA J. 46, 3012–3037 (2008)CrossRefGoogle Scholar
- 17.Toro, E.F., Vázquez-Cendón, M.E.: Flux splitting schemes for the Euler equations. Comput. Fluids 70, 1–12 (2012)MathSciNetCrossRefGoogle Scholar
- 18.Tiam, K.P., Tchuen, G.: A new flux splitting scheme based on Toro-Vazquez and HLL schemes for the Euler equations. J. Comput. Methods Phys. 2014, 1–13 (2014)CrossRefGoogle Scholar
- 19.Tiam, K.P., Tchuen, G.: An extension of the TV-HLL scheme for multi-dimensional compressible flows. Int. J. Comput. Fluid Dyn. 29(3–5), 303–312 (2015)MathSciNetGoogle Scholar
- 20.Tiam, K.P., Tchuen, G.: Numerical simulation of multi-dimensional inviscid compressible flows by using TV-HLL scheme. Chin. J. Aeronaut. 29(6), 1553–1562 (2016)CrossRefGoogle Scholar
- 21.Quirk, J.J.: A contribution to the great Riemann solvers debate. Int. J. Numer. Methods Fluids 18, 555–574 (1994)MathSciNetCrossRefGoogle Scholar
- 22.Janhunen, P.: A positive conservative method for magnetohydrodynamics based on HLL and Roe methods. J. Comput. Phys. 166, 649–661 (2000)MathSciNetCrossRefGoogle Scholar
- 23.Huang, K., Wu, H., Yu, H., Yan, D.: Cure for numerical shock instability in HLLC solver. Int. J. Numer. Methods Fluids 65, 1026–1038 (2011)CrossRefGoogle Scholar
- 24.Nishikawa, H., Kitamura, K.: Very simple, carbuncle-free, boundary-layer-resolving, rotated-hybrid Riemann solvers. J. Comput. Phys. 227, 2560–2581 (2008)MathSciNetCrossRefGoogle Scholar
- 25.Ren, Y.X.: A robust shock-capturing scheme based on rotated Riemann solvers. Comput. Fluids 32, 1379–1403 (2003)CrossRefGoogle Scholar
- 26.Tchuen, G., Tiam, K.P., Burtschell, Y.: An accurate shock-capturing scheme based on rotated-hybrid Riemann solver: AUFSRR scheme. Int. J. Numer. Methods Heat Fluid Flow 26(5), 1310–1327 (2016)MathSciNetCrossRefGoogle Scholar
- 27.Shen, Z., Ya, W., Yuan, G.: A stability analysis of hybrid schemes to cure shock instability. Commun. Comput. Phys. 15(5), 1320–1342 (2014)MathSciNetCrossRefGoogle Scholar
- 28.Toro, E.F.: Riemann Solvers and Numerical Methods for Fluid Dynamics, 2nd edn. Springer, Berlin (1999)CrossRefGoogle Scholar
- 29.Pandolfi, M., D’Ambrosio, D.: Numerical instabilities in upwind methods: analysis and cures for the “Carbuncle” phenomenon. J. Comput. Phys. 166, 271 (2001)MathSciNetCrossRefGoogle Scholar
- 30.Tchuen, G., Fogang, F., Burtschell, Y., Woafo, P.: Hybrid upwind splitting scheme by combining the approaches of Roe and AUFS for compressible flow problems. Int. J. Eng. Syst. Model. Simul. 3(1/2), 16–25 (2011)Google Scholar
- 31.Bazhenova, T.V., Gvozdeva, L.G., Nettleton, M.A.: Unsteady interactions of shock waves. Prog. Aerosp. Sci. 21, 249–331 (1984)CrossRefGoogle Scholar
- 32.Billett, S.J., Toro, E.F.: Unsplit WAF-type schemes for three dimensional hyperbolic conservation laws. In: Toro, E.F., Clarke, J.F. (eds.) Numerical Methods for Wave Propagation, pp. 75–124. Springer, Dordrecht (1998)CrossRefGoogle Scholar
Copyright information
© Springer Nature India Private Limited 2019